Velocity profiling in an extrusion apparatus

ABSTRACT

An apparatus has an extrusion head for extruding a bead of a liquified material at an extruded pump flow rate, an extrusion head motor for driving the extrusion head at a variable head velocity, a pump for providing liquified material to the extrusion head, and a control for providing control signals to both the extrusion head motor and the pump. The control signals control operation of the extrusion head and the pump so that the head velocity is slaved to an estimated profile of the extruded pump flow rate divided by a predetermined bead cross-sectional area.

CROSS-REFERENCE TO RELATED APPLICATION(S)

None.

BACKGROUND OF THE INVENTION

The present invention relates to computer controlled extrusion of aliquified material. One useful application for computer-controlledextrusion techniques is in rapid prototyping of models or objects. Inparticular, the present invention is an extrusion apparatus from which aliquified material is extruded at a variable extruded pump flow ratethat dictates the velocity profile of the extrusion apparatus.

A rapid prototyping system involves the making of three-dimensionalobjects based upon design data provided from a computer aided design(CAD) system. Examples of apparatus and methods for rapid prototyping ofthree-dimensional objects by depositing layers of solidifying materialare described in Crump U.S. Pat. No. 5,121,329, Batchelder et al. U.S.Pat. No. 5,303,141, Crump U.S. Pat. No. 5,340,433, Batchelder U.S. Pat.No. 5,402,351, Batchelder U.S. Pat. No. 5,426,722, Crump et al. U.S.Pat. No. 5,503,785, and Abrams et al. U.S. Pat. No. 5,587,913, all ofwhich are assigned to Stratasys, Inc.

A typical rapid prototyping system of the prior art has an extrusionhead for extruding a bead of a liquified material, an extrusion headmotor for driving the extrusion head, an extrusion pump for providingthe material to the extrusion head, and a control for providing controlsignals to both the extrusion head motor and the extrusion pump. Thecontrol signals control motion and velocity of the extrusion head andoperation of the extrusion pump.

The extrusion head is driven at a constant head velocity along a pathdefined by a series of vertices. This head velocity is preselected so asto accomplish the general goal of causing the extrusion head to quicklynavigate the path while minimizing the extrusion head's displacementfrom the path. As a result, the head velocity is preselected to equal asufficiently low value so that when the extrusion head proceeds throughany of the vertices where its heading is caused to change greatly, thedeviation by the extrusion head from the path, or following error, willbe contained within an allowable error allowance.

The liquified material delivered by the extrusion head has a bead of across-sectional area that should ideally be controlled to create anaccurate prototype. This bead size is related to both the extruded pumpflow rate, which is the rate at which material is extruded from theextrusion head, and to the extrusion head velocity. The bead size willincrease if the head velocity is held constant while the extruded pumpflow rate is increased. Conversely, the bead size will decrease if theextruded pump flow rate is held constant and the head velocityincreased. In the past, an unvarying bead width has generally beendesired; therefore, both the extruded pump flow rate and the extrusionhead velocity have remained constant as well.

While this method of holding both the head velocity and the extrudedpump flow rate constant allows for an unvarying bead width of materialto be extruded while keeping any displacement of the extrusion headwithin the allowable error allowance, there are several problems withthis method.

First, the extrusion head velocity is held at a constant valuesubstantially less than the maximum velocity at which the extrusion headcan be driven, thereby requiring a longer amount of time to create amodel than might otherwise be possible if the extrusion head were drivenat a greater velocity. This is particularly problematic in view of thegrowing demand for the creation of larger and more complex models.

Second, the extrusion head velocity cannot be slowed at any verticesthat might benefit from a slower head velocity. Although thedisplacement of the extrusion head from the path is contained within theallowable error allowance, the amount of displacement could be furtherreduced if the extrusion head velocity were reduced at these vertices.In addition, the tolerable error allowance could be reduced if headvelocity varied depending upon the characteristics of the path alongwhich the extrusion head is driven.

There is therefore a need for an extrusion system that can achieve agreater throughput and a better product by varying the head velocity ofthe extrusion head and causing the extrusion head to more quicklynavigate the predefined path.

BRIEF SUMMARY OF THE INVENTION

An apparatus has an extrusion head for extruding a bead of a liquifiedmaterial at an extruded pump flow rate, an extrusion head motor fordriving the extrusion head at a variable head velocity, a pump forproviding liquified material to the extrusion head, and a control forproviding control signals to both the extrusion head motor and the pump.The control signals control operation of the extrusion head and the pumpso that the head velocity is slaved to an estimated profile of theextruded pump flow rate divided by a predetermined bead cross-sectionalarea.

In a preferred embodiment, the control signal provided to pump are stepsignals that result in the estimated profile of the extruded pump flowrate fitting an exponential function. Accordingly, head velocity duringan acceleration phase is exponentially increased, as a function of apump acceleration time constant, and the head velocity during adeceleration phase is exponentially decreased, as a function of a pumpdeceleration time constant.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an exterior front elevation view of the preferred embodimentof the invention, showing the system in a build state.

FIG. 2 is an exterior elevation view of the right side of the preferredembodiment of the invention.

FIG. 3 is an exterior elevation view of the left side of the preferredembodiment of the invention.

FIG. 4 is a front elevation view of the prototyping envelope, showingthe system in a build state.

FIG. 5 is an electrical block diagram of the control system of thepreferred embodiment of the invention.

FIG. 6 is a partially exploded perspective view of the prototypingenvelope showing the modeling extrusion head in a build position.

FIG. 6A is a detailed view of a portion of FIG. 5 illustrating thevacuum platen grooves.

FIG. 6B is a detailed view of a portion of FIG. 5 illustrating the airbearing of the linear motor.

FIG. 7 is an exploded view of the filament spindle and filament spoolshown in FIGS. 2 and 3.

FIG. 7A is a perspective view of the outward face of the EEPROM board.

FIG. 8 is a front elevation of the modeling extrusion head, withportions shown in sectional.

FIG. 9 is an exploded view of the liquifier.

FIGS. 10A and 10B show an alternative embodiment of the liquifier.

FIGS. 11A, 11B, and 11C are graphs illustrating velocity and flowprofiles of the extrusion head.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the preferred embodiment, the present invention is used in a rapidprototyping system 10 in which three-dimensional objects are formed bydepositing layers of a solidifying material from a moveable extrusionhead. The rapid prototyping system 10 is contained within a cabinet 12,as shown in FIG. 1. The cabinet 12 has doors and covers located on afront, left and right sides thereof. On the front of cabinet 12, thereis an envelope door 14, a modeling waste tray door 16 to the right ofenvelope door 14, a touch screen display panel 21 to the right ofmodeling waste tray door 16, a support waste tray door 18 to the left ofenvelope door 14, and platform cover 20 below envelope door 14. Amodeling drybox door 22 and an electronics bay cover 24 are located onthe right hand side of cabinet 12. A support drybox door 26 is locatedabove a compressor bay cover 28 on the left hand side of cabinet 12.

The upper right hand side of cabinet 12 houses a modeling extrusionapparatus 30, which comprises a modeling extrusion head 32 attachedbelow a modeling x-y forcer 33 and connected to the end of a modelingarm 34 which rotates about a modeling pivot joint 36. Modeling extrusionapparatus 30 receives a filament of modeling material 40 from a modelingfilament spool 42 located in a modeling drybox 45 (FIG. 2) below pivotjoint 36 and accessible through modeling drybox door 22. Drybox 45maintains low humidity conditions to optimize the condition of filament40. Modeling extrusion apparatus 30 is used to dispense modelingmaterial in layers onto a substrate 60. Modeling filament spool 42mounted on a modeling spindle 43 in drybox 45 is more clearly shown inFIG. 2.

The left-hand side of cabinet 12 houses a support extrusion apparatus44, which is comprised of a support extrusion head 46 attached below asupport x-y forcer 52 and connected to the end of a support arm 48 whichrotates about a support pivot joint 50. Support extrusion apparatus 44receives a filament of support material 54 from a support filament spool56 located in a support filament drybox 57 (FIG. 3) beneath supportpivot joint 50 and accessible through support drybox door 26. Drybox 57maintains low humidity conditions to optimize the condition of filament54. Support extrusion apparatus 44 is used to dispense support materialin layers. Support filament spool 56 mounted on a support spindle 58 indrybox 57 is more clearly shown in FIG. 3.

Modeling material extruded in layers by modeling extrusion apparatus 30forms object 64. The support material is used to support anyover-hanging portions as the object is being built up. In building anobject, over-hanging segments or portions which are not directlysupported in the final geometry by the modeling material require asupport structure. Support filament 54 is supplied to support extrusionhead 46 which deposits material to provide the required support. Thesupport material, like the modeling material, is deposited in multiplelayers.

In building an object, only one extrusion apparatus at a time is in anactive, extruding state. In FIG. 1, the system 10 is shown building athree-dimensional object 64, with modeling extrusion apparatus 30 in anactive build state, and support extrusion apparatus 44 in a home restposition. When modeling extrusion apparatus 30 is in an active state,modeling filament 40 travels through arm 34 to extrusion head 32, whereis it heated to a liquid state. Layers of modeling material in a moltenstate are deposited by head 32 through a liquifier 59 protruding througha bottom surface of head 32, onto substrate 60. Substrate 60 issupported upon a vacuum platen 62 and held in place by vacuum forces.When support extrusion apparatus 44 is in an active build state, supporthead 46 similarly receives support filament 54 via arm 48, and heats itto a liquid state. Layers of support material in a molten state aredeposited by head 46 through a liquifier 59 protruding through a bottomsurface of head 32, onto substrate 60.

The filaments of modeling and support materials are each a solidmaterial which can be heated relatively rapidly above its solidificationtemperature, and which will solidify upon a drop in temperature afterbeing dispensed from the extrusion head. A composition having arelatively high adhesion to itself upon which it is deposited when hotis selected for the modeling material. A composition having a relativelylow adhesion to the model material upon which it is deposited isselected for the support material, so that the support material forms aweak, breakable bond with the modeling material and to itself. When theobject is complete, the support material is broken away by the operator,leaving the object formed of modeling material intact.

The modeling material is preferably a thermoplastic material. Othermaterials that may be used for the modeling material filament includebees wax, casting wax, machinable and industrial waxes, paraffin, avariety of thermoplastic resins, metals and metal alloys. Suitablemetals include silver, gold, platinum, nickel, alloys of those metals,aluminum, copper, gold, lead, magnesium, steel, titanium, pewter,manganese and bronze. Glass, and particularly Corning glass would alsobe satisfactory. Chemical setting materials, including two-part epoxieswould also be suitable. A modeling material found to be particularlysuitable is an acrylonitrile-butadiene-styrene (ABS) composition. Amaterial found to be particularly suitable for the support material isan acrylonitrile-butadiene-styrene (ABS) composition with a polystyrenecopolymer added as a filler (up to about 80%) to create a lower surfaceenergy of the ABS composition, and to provide a lower cohesion andadhesion of the material. Both filaments of material are preferably of avery small diameter, on the order of 0.070 inch. The filament may,however, be as small as 0.001 inch in diameter.

FIG. 4 shows a build envelope 70 which is the central interior region ofthe system 10, accessible through envelope door 14. In FIG. 4, door 14,platform cover 20, and the adjoining face plates of cabinet 12 areremoved. The envelope 70 is where a three-dimensional object is built.Envelope 70 contains a build platform 74 which comprises vacuum platen62 supported by a set of legs 76, which ride on a platform drawer 78.Build platform 74 moves vertically in a z-direction within envelope 70.Movement of build platform 74 is controlled by a z-drive chain 80,driven by a z-motor 114 (shown schematically in FIG. 5). Build platform74 remains stationary during formation of a single layer. As eachadditional layer is deposited on substrate 60, build platform 74 islowered slightly so as to allow a space for forming the subsequentlayer. Platform drawer 78 pulls forward to allow the operator readyaccess to vacuum platen 62.

An electrical system 90, shown schematically in FIG. 5, controls thesystem 10. A CPU 92, together with first input/output (IO) card 94 andsecond input/output (IO) card 96, control the overall operation of theelectrical system 90. CPU 92 receives instructions from the operatorthrough communication from touch screen display 21. Similarly, CPU 92communicates with touch screen display 21 to display messages for theoperator and to request input from the operator. CPU 92 in turncommunicates with IO cards 94 and 96. A power supply 98 supplies powerto electrical system 90.

Envelope heaters 100 and envelope blower 102 establish and maintain atemperature in the envelope 70 of approximately 80° C. An envelopethermal cutout (THCO) switch 108 carries current through the machine'smain contractor actuation coil. If the temperature reaches approximately120° C. the THCO switch opens and current through the main contractor tothe system is interrupted. The head blowers 104 and 106 supply air atambient temperature to cool the pathway of filaments 40 and 54 as theytravel into modeling extrusion head 32 and support extrusion head 46,respectively.

CPU 92 also controls a compressor 110. Compressor 110 suppliescompressed air alternately to x-y forcers 33 and 52 and to the vacuumthat is supplied to vacuum platen 62. CPU 92 provides layering drivesignals to selectively actuate the z-motor 114, which drives platform 74along the z-axis.

IO Card 94, under the control of CPU 92, sends and receives signalsassociated with modeling extrusion head 32 and the filament supplythereto. IO card 94 sends drive signals that control the movement andposition of x-y forcer 33. IO card 94 further sends and receives signalsto and from modeling extrusion head 32, which includes a thermocouple222 (TC), a heater 220 (HTR), a motor 246 (MTR) and a safety switch 210(SS) (shown in FIGS. 8-10). Safety switch 210 shuts down the system ifthe temperature in the modeling extrusion head 32 gets too high.

IO card 94 monitors data concerning modeling material filament spool 42through communications with a modeling drybox processor board 116.Modeling drybox processor board 116 is mounted inside of modelingfilament drybox 45. It receives data concerning the modeling filamentfrom a modeling filament sensor 118 (located at the inlet to filamentguide 236, shown in FIG. 8) and a modeling EEPROM board 120, which is acircuit board carrying an electronically readable and writeable device(EEPROM 188, shown in FIG. 7), attached to modeling material filamentspool 42. EEPROM board 120 acts as an electronic tag with a variety offunctions. It informs the control system 90 of the type of filament thatis on the spool and of the lineal feet of filament on the spool. Asfilament 40 is wound off of the spool 42, the CPU 92 keeps track of howmuch material was commanded to be extruded, subtracts this amount fromthe total on the EEPROM 188 and writes the new value to the EEPROM 188drybox. Preferably, the data on EEPROM board 120 is encrypted so that itcan be updated only by the CPU 92. Filament sensor 118 senses andindicates the presence or absence of filament at the entrance to thefilament feed tube. With filament remaining on the spool, the operatorcan then grab ahold of the filament and extract it from the extrusionhead 32. Unloading of the used filament and spool and reloading of a newspool is thereby made easier. CPU 92 receives the modeling filament datafrom IO card 94. At the outset of a job, the CPU 92 will calculatewhether a spool 42 or 56 contains enough filament to complete the job.Operator notification is then provided via touch screen display 21,stating either that the filament is adequate to complete the job, orthat the filament spool will need replacement and reloading during theprocess. Also at the outset of a job, the CPU verifies that the modelingfilament material on the spool is the same material specified in objectdata. If these materials are not the same, an operator notification isprovided via touch screen display 21, providing the operator anopportunity to switch spools.

IO card 94 additionally monitors the temperature in the envelope 70 viasignals received from envelope thermocouple 122, and it sends signals toand from a modeling head proximity sensor 124, a high-z proximity sensor126, a low-z proximity sensor 128 and an xyz noncontact tip positionsensor 130, all of which are described below.

IO card 96 serves similar functions as IO card 94, for the supportextrusion head 52 and the filament supply thereto. IO card 96 sendsdrive signals that control the movement and position of x-y forcer 52.IO card 96 further sends and receives signals to and from supportextrusion head 46, which includes a thermocouple (TC), a heater (HTR), amotor (MTR) and a safety switch (SS). The safety switch SS shuts downthe system if the temperature in the modeling extrusion head 46 gets toohigh.

IO card 96 monitors data concerning support material filament spool 56through communications with a support drybox processor board 132. Itreceives data concerning the support filament from a support filamentsensor 134 and a support EEPROM board 136, attached to support materialfilament spool 56. EEPROM board 136 acts as an electronic tag, in thesame manner as EEPROM board 120. CPU 92 receives the support filamentdata from support processor board 132, and uses it to provide operatorinformation in the same manner as described above with respect to themodeling filament.

IO card 96 further controls a first pressure valve 138 and a secondpressure valve 140, which alternately open and shut to direct the flowof air from compressor 110. When valve 138 is closed and valve 140 isopen, air from compressor 110 is directed to modeling head x-y forcer33. When valve 138 is open and valve 140 is closed, air from compressor110 is directed to support head x-y forcer 52. IO card 96 in additioncommunicates with support head proximity sensor 142, which is describedbelow.

To create an object using rapid prototyping system 10, an operator mustfirst power up the system by pressing a power on switch (not shown),located on touch screen display 21. The system 10 then enters amaintenance mode, in which the system executes a routine to calibratethe locations of modeling extrusion head 32, support extrusion head 46,and build platform 74. The calibration is done in two phases. In thefirst phase, the system initializes movement boundaries for theextrusion heads and the platform. Modeling head proximity sensor 124initializes boundaries of the modeling head 32, and support headproximity sensor 142 initializes boundaries of the support head 44.High-z proximity sensor 126 and low-z proximity sensor 128 togetherinitialize the boundaries of platform 74. In the second stage, the xyznoncontact tip position sensor 130 initializes the position of the tipsof liquifiers 59 and 65. The xyz noncontact tip position sensor 130 is amagnetic sensor imbedded in platform 74 which detects position of theliquifier tips with three displacement degrees of freedom.

After calibration is complete, the system exits the maintenance mode andenters a standby state. In the standby state, the design of athree-dimensional object 64 is input to CPU 92 via a LAN networkconnection (shown schematically in FIG. 5) utilizing CAD software suchas QUICKSLICE® from Stratasys, Inc., which sections the object designinto multiple layers to provide multiple-layer data corresponding to theparticular shape of each separate layer. After the layering data isreceived, the system 10 enters a warmup phase, during which the envelope70 is heated. Upon reaching a temperature of 80° C., the system enters abuild state during which it creates the three-dimensional object.

The modeling extrusion apparatus 30 is shown more particularly in FIG.6. Modeling extrusion apparatus 30 is movable in a horizontal plane in xand y directions. Modeling x-y forcer 33 is positioned beneath andparallel to a planar stator 150, which contains a grid of statorelements (not shown). Together x-y forcer 33 and planar stator 150 forman electromagnetic linear stepper motor 152. Commercially availablelinear stepper motor, are available from Northern Magnetics, Inc. ofSanta Clarita, Calif. The x-y forcer 33 consists of two sets ofsingle-axis forcers mounted at 90° to each other and permanent magnetswhich hold forcer 33 against the stator (not shown). A compressed airsupply 154, supplied by compressor 110, is provided to x-y forcer 33when modeling apparatus 30 is active. The compressed air supply 154flows upward through x-y forcer 33 and exits through a top surfacethereof, as is illustrated in FIG. 6B. The exiting air forms an airbearing 156 between x-y forcer 33 and planar stator 150, which allowsnearly frictionless motion of the forcer in a horizontal plane belowplanar stator 150. Drive signals to x-y forcer 33 are received throughan electrical supply 158 which powers a stepper motor driver locatedwithin x-y forcer 33 (not shown) to achieve motion. Ordinarily, linearstepper motors of this type exhibit abrupt jarring motions which createmechanical resonance. This resonance is problematic because the airbearing linear motor is under-damped and the motor may be driven withfrequency components that excite the natural frequency of the motor.Typically, use of such motors in high-precision systems such as rapidprototyping systems has thus been precluded. As described below, anumbilical to the head creates the surprising result of providing adamping effect sufficient to allow high-precision deposition at speedsfar exceeding those possible in prior art rapid prototyping systems.

Modeling extrusion arm 34 is a flexible chain carrier that is flexiblein a horizontal plane and substantially rigid in other directions. Arm34 carries within it air supply 154 and forcer electrical supply 158.Arm 34 also carries within it a modeling extrusion head electricalsupply 160 and a flexible air tube 162 which contains an ambient airsupply and modeling filament 40, as depicted in FIG. 8. Arm 34 togetherwith air supply 154, forcer electrical supply 158, extrusion headelectrical supply 160 and air tube 162 containing filament 40 form anumbilical 163 to extrusion head 32. The umbilical 163 creates thesurprising result of damping the mechanical resonance of extrusion head32 with respect to stator 30, which is produce by acceleration anddeceleration of the head 32 by forcer 33. In the preferred embodiment,the combined weight of head 32 and x-y forcer 33 is less than or equalto approximately 8 lbs.

The resonant frequency is about 55 Hz for small oscillations and about45 Hz for large oscillations, and the damping time to achieve 98% of thefinal value (which is equal to approximately 4 times the damping timeconstant) in this embodiment is less than or equal to about 150 ms.Oscillation and damping of mechanical resonance may be expressed as:A=A_(o) sin (ωt+Φ)e^(-t/)τ, where A=amplitude, A_(o) =initial undampedamplitude, w=2πf, f=resonant frequency of the system, Φ=a phaseconstant, t=time, and τ=damping time constant. Critical damping occurswhen τ=1/ω. In the preferred embodiment described, the system isapproximately a factor often from being critically damped. Furtherdamping can, therefore, be added if desired. The damping time constantis affected by the combined weight of extrusion head 32 and x-y forcer33. The lighter the weight, the shorter the damping time constant.

Damping of mechanical resonance is achieved primarily by frictionalforces produced during movement of umbilical 163. Alternatively, otherforms of damping means can be used, such as an oscillation dissipater(or shock-absorber) carried in extrusion head 32. Also, further dampingcan be produced by decreasing the resistivity of the bucking of starter150 (such as by using copper rather than steel) to increase eddy currentlosses within stator 150.

While FIG. 5 has been described as depicting modeling apparatus 30, itshould be understood that support head apparatus 44 has a similarstructure and has an umbilical of the same type described with referenceto modeling apparatus 30. Specifically, support x-y forcer 52 shares theplanar stator 150 such that x-y forcer 52 and stator 150 form a secondlinear motor. Support apparatus 44 starts from the opposite side ofcabinet 12 from modeling apparatus 30. For ease of reference, only onehead is shown in detail.

Vacuum platen 62 and substrate 60 are shown in an exploded fashion inFIG. 6. Vacuum platen 62 has a top surface 167 comprised of a grid ofgrooves 164, shown in detail in FIG. 6A. In the preferred embodiment,grooves 164 are 0.06 inches deep, 0.06 inches wide, and are 1 inch oncenter apart. An orifice 166 extends through the center of vacuum platen62. Orifice 166 receives a vacuum hose 168 which connects to vacuum pump112. When the system 10 is powered up, a vacuum is applied to vacuumplaten 62 by vacuum hose 168 and vacuum pump 112. The vacuum provided toplaten 62 pulls air through grooves 164 to distribute the vacuum alongthe platen. This vacuum holds the substrate 60 against the top surface167 of platen 62. In the preferred embodiment, substrate 60 is aflexible sheet. A polymeric material forms a suitable flexible sheetsubstrate. An acrylic sheet with a thickness of about 0.06 inches hasbeen successfully used as a substrate. When a desired object is formed,the operator can remove substrate 60 from the platen 62 by lifting onecorner of the sheet and breaking the seal of the applied vacuum.

Flexible substrate 60 can be flexed away from the object to peel thesubstrate from the object, if there is a weak breakable bond betweensubstrate 60 and the object. This weak, breakable bond may be formed bydepositing a first layer (or layers) of modeling material followed by asecond layer (or layers) of support material on the substrate 60. Themodeling material and substrate are selected so that the modelingmaterial is fully adhesive to the substrate. In forming an object, themodeling material is deposited in one or more layers on the substrate60. The support material is then deposited in one or more layers overthe modeling material. The object is then built up on the supportmaterial, using a plurality of layers of modeling and/or supportmaterial. When the object is complete, vacuum is broken by lifting acorner of the substrate 60, and the substrate 60 is removed from theplaten 62 by the operator. By flexing the substrate 60, the operatorthen peels the substrate 60 from the object. The first layer(s) ofmodeling material will remain adhered to the substrate, but the weakbond between the first layer(s) of modeling material and the secondlayer(s) of support material is a readily separable joint which breaksto allow removal of the substrate 60 without damage to the object.

Other flexible sheet materials may be used as substrate 60. For example,plain or coated paper, metal foil and other polymeric materials aresuitable. For high temperature support and modeling materials, apolymeric material (e.g., Kapton) or metal foil is particularlydesirable.

Although a vacuum is a preferred way to achieve a releasable hold downforce to hold substrate 60 against platen 62, other means for providinga releasable hold down force can also be used. For example, substrate 60can be held against platen 62 by an electrostatic chuck or by a weaklyadhering adhesive applied to the bottom surface of the substrate 60 orthe top surface of the platen 62 (or both).

FIG. 7 shows a detailed exploded view of the filament spool and spindleshown in FIGS. 2 and 3. The mechanical configuration of the filamentspool and spindle is identical for both the modeling filament and thesupport filament. For convenience of reference, FIG. 7 is directedspecifically to modeling filament spool 42 and modeling spindle 43.Spindle 43 extends horizontally from drybox 45 and has a semi-circularshape. A semi-circular connector 174 having a set of six depressibleconnector pins 176 is mounted on top of spindle 43 adjoining drybox 45.A spring-loaded latch 178 is embedded in the top of spindle 43 at anouter edge 179.

Filament spool 42 is comprised of a center barrel 180 on which filamentmay be wound, a pair of spool flanges 181 extending from either end ofbarrel 180, a sleeve 182 that fits within barrel 180 for receivingspindle 43, and modeling EEPROM board 120 mounted inside sleeve 182 andperpendicular to barrel 180. Barrel 180 rotates about sleeve 182 so thatfilament 40 may be unwound from spool 42. Sleeve 182 has a flange 184 atone end, a flange 186 at the opposite end, and an interior semi-circularcavity for receiving spindle 43. In the preferred embodiment, flange 184is removable and flange 186 is fixed. Removal of flange 184 allowswithdrawal of sleeve 182 from barrel 180. As mentioned above, EEPROMboard 120 carries EEPROM 188. In a preferred embodiment, EEPROM board120 is mounted adjacent fixed flange 186 by a pair of screws 190, sothat EEPROM 188 faces inward towards sleeve 182 for protection. EEPROMboard 120 on its outward facing side carries a set of six roundelectrical contacts 192, as shown in FIG. 7A. Connectors 192 areconfigured so as to provide a receiving surface for connector pins 176when spool 42 is mounted on spindle 43.

Latch 178 must be manually depressed to allow insertion or removal ofspindle 43 from sleeve 182. When sleeve 182 is mounted on spindle 43,latch 179 rests in an upward position so as to lock spool 42 into placesuch that contacts 192 fully depress connector pins 176. When filamentspool 42 is manually inserted onto spool holder 43, electrical contactbetween EEPROM board 120 and drybox processor board 116 is made throughthe connector 190.

Detail of the extrusion apparatus is shown in FIG. 8. While FIG. 8 showsmodeling extrusion apparatus 30, it should be understood that supportextrusion apparatus 44 contains the same parts and operates in the samemanner as modeling extrusion apparatus 30, at a 180° rotation. Extrusionhead 32 is mounted below x-y forcer 38 by a pair of mounting plates 200.Two pairs of bolts 202 attach head 32 to plates 200. Two bolts 204connect plates 200 to x-y forcer 38 to hold head 32.

Extrusion head 32 is formed of an enclosure 206 which holds liquifier59, a filament drive 208 and safety switch 210. Liquifier 59 comprises athermal conducting thin-wall tube 212, a heating block 214, an extrusiontip 216, a tip retainer 218, heater 220 and thermocouple 222. FIG. 9shows liquifier 59 in an exploded view. As shown in FIG. 9, thin-walltube 212 has an inlet end 224, an outlet end 226, and is bent at a 90°angle. In the preferred embodiment, tip 216 is soldered into the outletend of tube 212. Alternatively, tip 216 may be brazed or welded to tube212. Or, a nozzle may be formed in the tube itself by swaging the outletend 226 of the tube. Using a 0.070 inch filament, tube 212 preferablyhas an inner diameter of about 0.074 inches. The wall thickness of tube212 is preferably between 0.005-0.015 inches. It is desirable to keeptube 212 as thin as possible to achieve maximum heat transfer acrosstube 212 to filament 40. In the preferred embodiment, tube 212 is madeof stainless steel. Other metals may also be used, such as brass,copper, tungsten, titanium, molybdenum, beryllium copper or othersteels. Other thermal conducting materials such as polymide (Kapton), aplastic with a high melting temperature, may also be used to form thethin-wall tube.

Tube 212 fits into a channel 229 of heating block 214, between a frontsection 228 and a rear section 230 of the heating block. Heating block214 is made of a heat conductive material such as aluminum or berylliumcopper. A set of four bolts 232 extend through outer section 228 andrear section 230 of heating block 214 to hold tube 212. When mounted inheating block 214, a first section of tube 212 adjacent the inlet end224 is exterior to heating block 214, and a second mid-section of tube212 is clamped within heating block 214, and a third section of tube 212including tip 216 extends through the bottom of block 214. The firstsection of tube 212 forms a cap zone for the liquifier 59, the secondsection of tube 212 forms a heating zone, and the third section forms anozzle zone. The nozzle zone is contained within and silver soldered toextrusion tip 216, which is supported against heating block 214 by tipretainer 218, a square plate having a center orifice. Tip retainer 218is press fit around the extrusion tip 216, and mounted beneath heatingblock 214 by a pair of screws 234.

The length of the cap zone of tube 212 is in the range of 0.15 inchesand 2 inches. The cap zone must undergo a temperature gradient fromabout 70 degrees C envelope temperature to about 280 degrees C liquifiertemperature. A shorter cap zone allows for greater control by the systemover the rate that molten filament is extruded (i.e., flow rate), butmakes it more difficult to maintain a cool temperature for the filamentthrough the cap zone. The length of the heating zone is anywhere from0.04 inches to 7 inches. The longer the heating zone, the higher themaximum extruded flow rate, but the slower that the flow rate can beaccelerated and decelerated. A liquifier having a cap zone of between0.02-0.04 inches long and a heating zone of about 2.5 inches long hasbeen successfully used in a preferred embodiment of the system.

Cylindrical heater 220 and thermocouple 222 extend horizontally intorear section 230 of heating block 214. Heater 220 is positioned in heatexchange relation to the heating zone of tube 212, to heat the tube to atemperature just above the melting temperature of the filament. Using anABS composition for the filament 40, the tube is heated to about 270degrees C. Thermocouple 222 is positioned adjacent tube 212 to monitorthe temperature in the tube. Safety switch 210 will cause the system 10to shut down if temperature exceeds a predetermined level.

A guide tube 236 guides filament 40 from pivot 36 to extrusion head 32,made of a suitable low friction material such as Teflon for support inmotion. As described above, filament 40 within guide tube 36 are locatedwithin flexible tube 60 contained inside of arm 34. Filament 40 entersextrusion head 32 through an inlet aperture 238. Inside of extrusionhead 32, filament 40 is fed through a tapered guide 240 having arestricted guide passage 242. Filament drive 208 is comprised of astepper motor 246, a pulley 248 and a pair of feed rollers 250 and 252.Roller 250 has a drive shaft 254 which is driven by stepper motor 246.Roller 252 is a rubber-coated idler. Filament 40 is fed from the guidepassage 242 of tapered guide 240 into a nip between rollers 250 and 252.The rotation of roller 250 advances filament 40 towards liquifier 59.The inlet end 224 of thin-wall tube 212 is positioned to receivefilament 40 as it passes through rollers 250 and 252. The flow rate ofthe molten filament out of liquifier 59 is controlled by the speed atwhich filament drive 208 advances the filament 40 into liquifier 59.

A blower 256 blows air at ambient temperature into flexible tube 60 tocool guide tube 236 and filament 40. Cooling of strand 40 is importantso as to maintain the filament at a sufficiently low temperature that isdoes not become limp and buckled within the passages leading into theliquifier 59. Air from blower 256 travels through tube 60 and entersextrusion head 32 via an air conduit 258. Air conduit 258 provides apath for the air which is in a forward and parallel position fromfilament 40 within extrusion head 32.

FIGS. 10A and 10B show an alternative embodiment of the liquifier. FIG.10A shows liquifier 259 in an assembled view, while 10B shows liquifier259 in an exploded view. In this embodiment, two thin-wall tubes 260Aand 260B of the type described above flow into one, nozzle 262. Aliquifier of this type can be substituted into the dispensing head shownin FIG. 8 to provide one extrusion head that dispenses, at alternatetimes, two different deposition materials. The two deposition materialsmay be a modeling and a supply material, or they may be modelingmaterials of two different colors or having other diverse properties.Nozzle 262 is brazed or welded to the outlet ends 264 of tubes 260A and260B. Nozzle 262 is positioned in a vertical orientation, while tubes260A and 260B may be angled towards the horizontal. Separate feedmechanisms (not shown) are provided for tubes 260A and 260B so thatfilament material is fed into only one of the tubes at any given time.

Thin-wall tubes 260A and 260B are held into position by a heating block266. Heating block 266 is comprised of an outer plate 268, an interiorplate 270 and a rear plate 272. Rear plate 272 is mounted within theextrusion head, and holds a heater 274 which extends between tubes 260.Two channels 276 which hold tubes 260A and 260B are routed throughinterior block 270. A set of five bolts (not shown) extend through outerplate 268, interior plate 270 and rear plate 272 to detachably holdtogether liquifier 259. It is an advantageous that the liquifier beremovable from the heating block, for replacement and cleaning.

Velocity Profiling

In a preferred embodiment of rapid prototyping system 10, the velocityof both modeling extrusion head 32 and support extrusion head 46 ismaintained proportional to the flow rates of modeling and supportmaterial extruded by each head, respectively. Slaving head velocity toflow rates allows control over the bead size of extruded material whileachieving a high throughput.

The present description focuses on modeling extrusion head 32, but itshould be understood that the velocity control of the present inventionapplies equally to support extrusion head 42. It should further beunderstood that the teachings of the present invention are applicable toother robotic systems which perform extrusions using a movable extrusionhead.

Modeling extrusion head 32, carrying liquifier 59, moves at a variablehead velocity V_(H) in x and y directions. CPU 92 controls head velocityV_(H) by controlling linear stepper motor 152 which drives extrusionhead 32. Extrusion head 32 delivers liquified filament 40 at a variableextruded pump flow rate Q_(P). The extruded pump flow rate Q_(P) isdependent on the time response of liquifier 59 in providing or ceasingto provide liquified filament, represented by a time constant τ, andupon a velocity V_(D) at which filament drive 208 operates to advancefilament 40 into liquifier 59. Together, filament drive 208 andliquifier 59 form a pump which provides liquified filament forextrusion, at a rate that determines pump flow rate Q_(P). CPU 92controls extruded pump flow rate Q_(P) by providing control signals tostepper motor 146 which drives filament drive 208.

The material extruded by extrusion head 32 has a bead size that isrelated to both the extruded pump flow rate Q_(P) and the extrusion headvelocity V_(H). In a typical application, it is desired that the beadsize remain constant, although applications may arise where it isdesired that bead size vary according to, for example, a sinusoidalfunction.

Movement of extrusion head 32 is more quickly and easily controlled thanthe rate at which material is extruded by the extrusion head 32.Additionally, in an open-loop system such as rapid prototyping system10, there is no feedback measuring actual flow rate, so extruded pumpflow rate Q_(P) is estimated using experimental methods. The velocityprofiles of the present invention thus coordinate head velocity V_(H)with operation of the extrusion pump (liquifier 59 together withfilament drive 208, in the preferred embodiment described), maintainingextrusion head velocity V_(H) proportional to an estimated profile ofthe extruded pump flow rate Q_(P).

The estimated profile of extruded pump flow rate Q_(P) and the liquifiertime constant τ may be obtained using any number of possible methodsknown to those skilled in the art. It should be understood that the flowrate profile is unique to a given extrusion system. In the preferredembodiment described herein, experimentation has yielded that, for astep input control of stepper motor 246 of filament drive 208, extrudedpump flow rate Q_(P) has a response that fits to an exponential functiondependent upon the liquifier time constant. Accordingly, in thepreferred embodiment described herein, velocity of extrusion head 32 iscontrolled according to the estimated exponential profile of extrudedpump rate Q_(P). The flow rate profile for a given extrusion system mayalternatively be fitted to other types of time-responsive functions, forexample, a polynomial function.

FIGS. 11A, 11B, and 11C are graphs illustrating respectively filamentdrive velocity V_(D), extruded pump flow rate Q_(P) and extrusion headvelocity V_(H) as extrusion head 32 proceeds through a path composed ofa start point, a vertex point, and a stop point. It should be understoodthat the path followed by extrusion head 32 would generally comprisemultiple vertices. The points along the path are generated by amove-compiler (not shown) in a known manner, and provided to CPU 92. Themove-compiler also determines and provides to CPU 92 for each vertex avertex velocity V_(V), which is the maximum velocity at which extrusionhead 32 can be driven through that vertex without exceeding an allowableerror. In moving extrusion head 32 through the path, CPU 92 ideallyaccelerates head velocity V_(H) toward a steady-state velocity V_(SS),decelerates head velocity V_(H) to zero velocity, or adjusts headvelocity V_(H) to achieve a vertex velocity V_(V). As shown in FIG. 11A,filament drive 208 is generally either off or operating at steady-statevelocity V_(SS).

The rapid prototyping system 10, as with other robotic extrusionsystems, goes through four extrusion phases (pre-pump, acceleration,deceleration, and suck-back), each of which are also illustrated inFIGS. 11A, 11B, and 11C. As described below, the velocity profiles ofthe present invention are specific to each of the four phases.

The first phase that the system goes through is the pre-pump (orcharging) phase. Upon initially engaging filament drive 208, there is apre-pump time delay T_(PP) before any material is extruded from theextrusion pump. During this pre-pump phase, extrusion head 32 is notextruding any material and, therefore, extrusion head 32 is heldmotionless (V_(H),PP =0). To minimize delay T_(PP), filament drive 208runs at a pre-pump velocity V_(D),PP that is greater than steady-statevelocity V_(SS).

The acceleration phase begins once extrusion head 32 begins extrudingmaterial. The goal of the acceleration phase is to accelerate headvelocity V_(H) until it reaches the steady-state velocity V_(SS). Attimes, however, head velocity V_(H) must be stopped before reachingsteady-state velocity V_(SS) at an intermediate velocity V_(I) becausereaching steady-state velocity V_(SS) would make it impossible todecelerate fully to the vertex velocity V_(V) associated with the nextvertex. This intermediate velocity V_(I) is the maximum velocity fromwhich the head velocity V_(H) can be decelerated to reach the velocitydesired at the next vertex. During this phase, velocity V_(D) offilament drive 208 is held at steady-state velocity V_(SS). In responseto filament drive 208 being run at the steady-state velocity V_(SS),pump flow rate Q_(P) increases exponentially. Extruded pump flow rateQ_(P) can be modeled by the following equation:

    Q.sub.P,A (t)=Q.sub.SS (1-e.sup.-t/τ.sbsp.A)

where Q_(SS) is the steady-state flow rate and τ_(A) is the accelerationtime constant that defines the exponential increase in pump flow rateQ_(P). The steady-state flow rate Q_(SS) is defined as the maximum rateat which extrusion head 32 can extrude the liquified filament ofmaterial. As in a typical exponential system, the length of timerequired for extruded pump flow rate Q_(P) to increase from zero tosteady-state flow rate Q_(SS) is approximately five acceleration timeconstants τ_(A). In a preferred embodiment of the present invention,acceleration time constant τ_(A) is less than 0.05 seconds, allowing forthe pump flow rate to be rapidly increased.

Since head velocity V_(H) is slaved to extruded pump flow rate Q_(P),head velocity V_(H) is similarly defined by the following equation:

    V.sub.H,A (t)=V.sub.SS (1-e.sup.-t/τ.sbsp.A)

where steady-state velocity V_(SS) equals steady-state flow rate Q_(SS)divided by the desired cross-sectional area of the bead extruded byextrusion head 32.

The acceleration of extrusion head 32, during the acceleration phase, isdefined by the following equation: ##EQU1## where V_(SS) /τ_(A) is themaximum acceleration of extrusion head 32.

Once modeling extrusion head 32 reaches either the steady-state velocityV_(SS) or the intermediate velocity V_(I), extrusion head 32 enters thedeceleration phase, where filament drive 208 is turned off. The goal ofthe deceleration phase is to decelerate head velocity V_(H) until itreaches either zero or, if applicable, vertex velocity V_(V). During thedeceleration phase, extruded pump flow rate Q_(P) decreasesexponentially, as defined by the following equation:

    Q.sub.P,D (t)=Q.sub.SS e.sup.-t/τ.sbsp.D

where τ_(D) is the deceleration time constant that defines theexponential decrease in pump flow rate Q_(P). In a preferred embodimentof the present invention, deceleration time constant τ_(D) is less than0.05 seconds, allowing for the pump flow rate to be rapidly decelerated.The time constant associated with liquifier 59 may remain constantthroughout each phase of the system; however, the time constant may alsohave a different value for each phase. In a system in which the timeconstant remains constant regardless of phase, the acceleration timeconstant τ_(A) and the deceleration time constant τ_(D) in the aboveequations could be replaced with a singular time constant τ.

Similarly, the following equation defines the velocity profile ofmodeling extrusion head 32 during the deceleration phase:

    V.sub.H,D (t)=V.sub.SS e.sup.-t/τ.sbsp.D.

The acceleration of extrusion head 32, during the deceleration phase, isdefined by the following relationship: ##EQU2##

Finally, the suck-back phase is employed as modeling extrusion head 32approaches a stop. During the suck-back phase, filament drive 208reverses direction and operates at a constant suck-back velocity V_(SB)to prevent excess material from being extruded. Unlike in the pre-pumpphase, modeling extrusion head 32 must continue moving during thesuck-back phase to maintain a consistent bead size.

During the suck-back phase, extruded pump flow rate Q_(P) continues tobe accurately modeled by the deceleration phase exponential profile.Similarly, the velocity profile of extrusion head velocity V_(H) remainsthe same as that of the deceleration phase. Because it would takeinfinitely long for extrusion head velocity V_(H) to reach zero whenfollowing an exponential profile, the exponential head velocity profileis replaced with a linear profile for extrusion head velocities V_(H)not exceeding a suck-back trip velocity V_(SBT). Once extrusion headvelocity V_(H) reaches suck-back trip velocity V_(SBT), extrusion headvelocity is changed from the suck-back exponential profile, which isidentical to the deceleration phase exponential profile, to thesuck-back phase linear profile:

    V.sub.H,SB (t)=V.sub.SBT +A.sub.SB t

where A_(SB) is the slope of the linear profile. A_(SB) can becalculated as the negative of the initial acceleration in head velocityV_(H) during the acceleration phase.

EXAMPLE

If rapid prototyping system 10 were to have the specifications of Q_(SS)=1786 μin³ /sec, V_(SS) =10 in/sec, τ_(A), τ_(D) =τ=0.025 seconds,V_(SBT) =0.3 in/sec, and A_(SB) =-400 in/sec², the extruded pump flowrate Q_(P) and the extrusion head velocity V_(H) would be representedwith the following equations:

Pre-pump Phase

    Q.sub.P,PP (t)=0

    V.sub.H,PP (t)=0

Acceleration Phase

    Q.sub.P,A (t)=(1786 μin.sup.3 /sec)(1-e.sup.-t/0.025 sec)

    V.sub.H,A (t)=(10 in/sec)(1-e.sup.-t/0.025 sec)

Deceleration Phase

    Q.sub.P,D (t)=(1786 μin.sup.3 /sec)(e.sup.-t/0.025 sec)

    V.sub.H,D (t)=(10 in/sec)(e.sup.-t/0.025 sec)

Suck-back Phase

    Q.sub.P,SB (t)=(1786 μin.sup.3 /sec)(e.sup.-t/0.025 sec)

    V.sub.H,D (t)=(10 in/sec)(e.sup.-t/0.025 sec) (for V.sub.H,SB ≦V.sub.SBT)

    V.sub.H,SB (t)=(0.3 in/sec)-(400 in/sec.sup.2)t (for V.sub.H,SB >V.sub.SBT)

While the above equations describe a velocity profile having applicationto the rapid prototyping system 10 described herein and for which aconstant bead size is desired, the velocity profiling of the presentinvention may also be applied to achieve a bead having a size thatvaries over time according to a preselected function L(t). In such acase, velocity V_(SS) in Equations 1 and 2 is replaced with atime-varying velocity profile V_(T) defined by the following equation:##EQU3##

It should also be understood that while the present invention has beendescribed in the context of a rapid prototyping system as the preferredembodiment, the velocity profiling of the present invention hasapplication in other rapid prototyping systems, as well as in roboticextrusion systems used in other fields. In such other systems, theextrusion pump may be other than the liquifier and filament drive of thepreferred embodiment described. For example, the extrusion pump may beany flow motivator, including a piston pump, viscosity pump,displacement pump, centripetal pump or an acoustic pump. The extrudedpump flow rate in such system, can be measured experimentally to obtainan estimated flow rate profile as discussed herein, and the extrusionhead velocity slaved to the estimated profile according to the presentinvention. Other fields in which velocity profiling can be appliedinclude adhesive dispensing applications (e.g., assembly of cars,diapers, boxes and clothing) and solder paste extrusion (used, forexample, in fabrication of circuit boards).

Although the present invention has been described with reference topreferred embodiments, workers skilled in the art will recognize thatchanges may be made in form and detail without departing from the spiritand scope of the invention.

We claim:
 1. An apparatus comprising:an extrusion head for extruding abead of a liquified material at an extruded pump flow rate; an extrusionhead motor for driving the extrusion head at a variable head velocity; aliquifier for liquifying the filament of material; a filament drive forproviding the filament of material to the liquifier; and a control forproviding control signals to both the extrusion head motor and thefilament drive, the control signals controlling operation of theextrusion head and the filament drive so that the head velocity isproportional to an estimated profile of the extruded pump flow rate. 2.The apparatus of claim 1 wherein the control provides a step signal asthe control signal to the filament drive to cause the extruded pump flowrate to have an exponential response.
 3. The apparatus of claim 2wherein:the control causes the head velocity during an accelerationphase to be exponentially increased, as a function of a liquifieracceleration time constant; and the control causes the head velocityduring a deceleration phase to be exponentially decreased, as a functionof a liquifier deceleration time constant.
 4. The apparatus of claim 3wherein the control causes the head velocity during the accelerationphase to be exponentially increased towards a steady-state headvelocity.
 5. The apparatus of claim 4 wherein the control causes thehead velocity during the acceleration phase to be selectively stopped atan intermediate velocity that is less than a steady-state velocity. 6.The apparatus of claim 3 wherein the control causes the head velocityduring the deceleration phase to be exponentially decreased to zero. 7.The apparatus of claim 3 wherein the control causes the head velocityduring the deceleration phase to be exponentially decreased to a vertexvelocity that is less than a steady-state velocity.
 8. The apparatus ofclaim 3 wherein:the control causes head velocity during a pre-pump phaseto be zero; and the control causes head velocity during a suck-backphase to be exponentially decreased towards zero, as a function of theliquifier deceleration time constant.
 9. The apparatus of claim 8wherein:the control causes head velocity to be linearly decreased tozero after head velocity reaches a suck-back trigger velocity during thesuck-back phase.
 10. The apparatus of claim 3 wherein the liquifieracceleration time constant is less than or equal to about 0.05 seconds.11. The apparatus of claim 3 wherein the liquifier deceleration timeconstant is less than or equal to about 0.05 seconds.
 12. An apparatuscomprising:an extrusion head for extruding a bead of a liquifiedmaterial at an extruded pump flow rate; an extrusion head motor fordriving the extrusion head at a variable head velocity; a pump forproviding liquified material to the extrusion head; and a control forproviding control signals to both the extrusion head motor and the pump,the control signals controlling operation of the extrusion head and thepump so that the head velocity is slaved to an estimated profile of theextruded pump flow rate divided by a predetermined bead cross-sectionalarea.
 13. The apparatus of claim 12 wherein the control provides stepcontrol signals to the pump to cause the estimated profile of theextruded pump flow rate to fit an exponential function.
 14. Theapparatus of claim 13 wherein:the control causes head velocity during anacceleration phase to be exponentially increased towards a steady-statehead velocity, as a function of a pump acceleration time constant; andthe control causes head velocity during a deceleration phase to beexponentially decreased towards zero, as a function of a pumpdeceleration time constant.
 15. The apparatus of claim 14 wherein thepump comprises a liquifier that receives and liquifies a filament ofmaterial and a filament drive that receives the control signals andresponsively provides the filament of material to the liquifier.
 16. Theapparatus of claim 15 wherein the pump acceleration time constant isless than or equal to about 0.05 seconds.
 17. The apparatus of claim 15wherein the pump deceleration time constant is less than or equal toabout 0.05 seconds.
 18. The apparatus of claim 14 wherein the controlcauses the head velocity during the acceleration phase to be selectivelystopped at an intermediate velocity that is less than a steady-statevelocity.
 19. The apparatus of claim 14 wherein the control causes thehead velocity during the deceleration phase to be exponentiallydecreased to a vertex velocity that is less than a steady-statevelocity.
 20. The apparatus of claim 14 wherein:the control causes headvelocity during a pre-pump phase to be zero; and the control causes headvelocity during a suck-back phase to be exponentially decreased towardszero, as a function of the pump deceleration time constant.
 21. Theapparatus of claim 20 wherein:the control causes head velocity to belinearly decreased to zero after head velocity reaches a suck-backtrigger velocity during the suck-back phase.
 22. In an apparatus havingan extrusion head for extruding a liquified material at an extruded pumpflow rate, an extrusion head motor for moving the extrusion head at avariable head velocity, and a control for providing control signalinputs to the extrusion head motor, a method for extruding the liquifiedmaterial in a bead having a predetermined cross-sectional area, themethod comprising the step of:controlling the head velocity according toan estimated profile of the extruded pump flow rate divided by thepredetermined bead cross-sectional area.
 23. The method of claim 22wherein the estimated profile of the extruded pump flow rate fits anexponential function, and the step of controlling the head velocitycomprises the steps of:exponentially increasing the head velocity duringan acceleration phase; and exponentially decreasing the head velocityduring a deceleration phase.
 24. The method of claim 23 and furthercomprising the steps of:maintaining the head velocity at zero during apre-pump phase; exponentially decreasing the head velocity during asuck-back phase; and linearly decreasing the head velocity to zero afterthe head velocity reaches a suck-back trigger velocity during thesuck-back phase.